- Docente: Armando Bazzani
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Moduli: Armando Bazzani (Modulo 1) Giorgio Turchetti (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Physics (cod. 8025)
Also valid for Second cycle degree programme (LM) in Physics of the Earth System (cod. 8626)
Learning outcomes
The aim of the course is to provide the tools to build up dynamical models for the evolution of the classical physical systems formed by interacting particles under the influence of external fields.
There will be explained numerical techniques for the solution of the corresponding differential equation even in the case of fluctuating fields. In the limit of a large number of particles there will be developed the kinetic and the fluid approximations. In the case of long range interactions the average field equations will be considered, together with self-consistent solutions
and collision models based on stochastic processes.
Course contents
Basic numerical methods: recurrences techniques and their convergence, Newton and bisection methods. Interpolation and numerical derivation and integration. Solution for linear equations.
Functions approximation. Finite difference methods for parabolic and wave equations.
Hamiltonian systems: Canonical transformations. Liouville equations. Perturbation theory and adiabatic limit. Symplectic maps and symplectic integrators.
Physical models: time dependent pendulum, three bodies problem, electromagnetic lens.
Stochastic systems: particle dynamics in a fluctuating field. Wiener noise and Langevin equation. Fokker-Planck equation. Master equation and thermodynamics formalism.
Models: stochastic oscillator, bistable systems, Markov models.
Extensive systems : kinetic equation for hard spheres. Vlasov equation for long range interactions. Collisions, stochastic diffusion processes and Boltzmann equilibrium. Distribution moments and fluid description.
Models: elastic rope, Burger viscous fluid, plasma waves.
Readings/Bibliography
G. Turchetti Appunti per Metodi e Modelli Numerici e libro Dinamica Classica http://www.physycom.unibo.it/corsi.php.
W. H. Press et al Numerical recipes per parte 1 V.I.Arnold Meccanica Classica Editori Riuniti per parte 2.
Gardiner Handbook of Stochastic Methods Springer per parte 3.
R. Balescu Equilibrium and Non-equilibrium Statistical Mechanics Wiley Interscience publication 1975.
A.Vulpiani Caos and coarse graining in statistical mechanics per parte 4.
Teaching methods
frontal lessons
numerical laboratory
Assessment methods
oral exam and project discussion
Teaching tools
slide projector
numerical hardware
Office hours
See the website of Armando Bazzani
See the website of Giorgio Turchetti